19 UNCERTAINTY AND INFORMATION Answers to the Problems 1. a. Lee’s expected income is $2,000 a month. Lee’s expected income is (0.5)($4,000) + (0.5)($0) = $2,000 a month. b. Lee’s utility is 50 units. When Lee’s income is $4,000, her utility is 100. When Lee’s income is $0, her utility is 0. So Lee’s expected utility is (0.5)(100) + (0.5)(0) = 50. c. Lee would have to be offered about $1,300 a month with certainty to persuade her not to take the risky job. Lee would have to be offered the income that would give her with certainty 50 units of utility. This income is read from the graph at the 50 units on the y-axis. 2. a. Jimmy’s expected utility is (0.5)(393) + (0.5)(0) = 196.5. Zenda’s expected utility is (0.5)(683) + (0.5)(0) = 341.5. b. The table sets out their marginal utility of wealth. Wealth Jimmy’s utility Jimmy's marginal utility Zenda's utility Zenda’s marginal utility 0 0 0 2.00 5.12 100 200 512 1.00 1.28 200 300 640 0.50 0.32 300 350 672 0.25 0.06 400 375 678 0.12 0.03 500 387 681 0.06 0.02 600 393 683 0.03 0.01 700 396 684 c. Zenda is more risk adverse. Zenda is more risk adverse than Jimmy because Zenda’s marginal utility of wealth decreases more quickly than does Jimmy’s. The table sets out their marginal utility of wealth. d. Zenda is more likely to buy insurance because she is more risk averse.

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2 3. Jimmy puts his money into the project, but Zenda does not. Jimmy maximizes his expected utility. If Jimmy puts his money into the project and it makes a profit, his utility is 393; if Jimmy puts his money into the project and it fails, his utility is 300. So Jimmy’s expected utility from the project is (0.85)(393) + (0.15)(300), which equals 379. If Jimmy keeps his $400 and does not join the project, his utility is 375. Jimmy will choose to join the project. Zenda maximizes her expected utility. If Zenda puts her money into the project and it makes a profit, her utility is 683; but if Zenda puts her money into the project and it fails, her utility is 640. So Zenda’s expected utility from the project is (0.85)(683) + (0.15)(640), which equals 676. If Zenda keeps her $400 and does not join the project, her utility is 678. Zenda will choose not to join the project. 4.

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